TU counting as an attack isn't even remotely intuitive. There is absolutely nothing in the wording that would indicate it's an attack, and even if it were, there still isn't necessarily a good reason for it to deal damage.
Basically the way I view damage is this:
Doll has X hp.
Doll takes D damage.
Doll now had X - D damage.
When you TU it, there isn't ever a point where it's at a higher HP, so it's never dealt damage.
This is a bit of a tangent, but it dealing damage isn't consistent with the functioning of the rest of the effects either . If damage is going to be dealt than I should also redeal any poison counters, refreeze weapons, etc.
We could argue about it more but basically the problem is that the wording isn't clear. This is shown by the number of people who have to have it explained to them what happened when they took damage. Why not change the wording a bit to make it more clear?